Suppose that in the figure below the transmission axes of the firSt and third li

Question

Suppose that in the figure below the transmission axes of the firSt and third linear polarizers are perpendicular to each other. In addition, let the second (center) linear polarizer rotate on the common axis with an angular speed omega. Show that if unpolarized light is incident on the first linear polarizer with an intensity I_max, the intensity of the light beam emerging from the third linear polarizer is I = 1/16I_max(1-cos4omegat). Hence, the intensity of the emerging light beam is modulated at a rate that is 4 times the rate of rotation of the second linear polarizer.

Explanation / Answer

Let theta = x   and   I(max) = Io   for simplification.

As x = wt

Intensity after first polarizer = Io/2

Intensity after second polarizer = (Io/2)*cos^2(wt)

Intensity after third polarizer = I = (Io/2)*cos^2(wt)*cos^2(90 - wt)

   I = (Io/2)*cos^2(wt)*sin^2(wt) = (Io/8)*(1 + cos2x)* (1 - cos2x)

   I = (Io/8)*(1 – cos^2(2x)) = (Io/8)*(sin^2(2x)) = (Io/16)(1 – cos4x)

Hence I = (I(max)/16)* (1 – cos4wt)

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